Patent document 1 shows an apparatus for determining a misfire during the warming-up operation of an engine according to a rotation change parameter indicative of changes in the engine rotational speed. According to this apparatus, the rotation change is calculated corresponding to the ignition timing of each cylinder, and a rotation change difference Nxd360 and a rotation change difference Nxd720 are further calculated. The rotation change difference Nxd360 is a difference between the rotation change of 360 degrees of the crank angle before and the present rotation change. The rotation change difference Nxd720 is a difference between the rotation change of 720 degrees of the crank angle before and the present rotation change. The misfire determination is performed based on the rotation change differences Nxd360 and Nxd720.